I have a friend who buys glass jugs of unpasteurized cider/juice from the orchard, takes off the cap, pops an airlock on, and waits for the yeast that was on the skins to kick in. It sounds risky, but he swears by the stuff!
–
Room3Mar 16 '10 at 18:19

The basic routine is to sanitize all of your equipment (follow instructions on package), dump the juice in the fermentation vessel, shake it for about a minute to get some oxygen in there, rehydrate the yeast (follow directions on packet), dump the yeast in and seal it up with an airlock. Wait a few weeks until the liquid clears (is not cloudy). After that, start a siphon with the tubing (a racking cane is cheap and extremely helpful, but not strictly required) to transfer the cider from the fermentation vessel to the bottles. The bottles need to be sanitized before using. Leave the sediment behind while transferring. Seal or cap bottles. If you want sparkling cider you can add carbonation drops to the bottles, or dissolve additional sugar in the cider before bottling (3/4 cup is about right). If you add additional sugar it is helpful to first transfer the cider to a second clean, sanitized vessel so you can leave the sediment behind in the first. If you made sparkling cider you'll have to keep the bottles in a warm place for 2-3 weeks to let it carbonate. Still cider will be ready immediately. Both will improve greatly with age.

NOTE: home-made cider is very dry and does not taste like commercial examples. To some it is an acquired taste. If you think it lacks apple-y flavor at first, let it age for a month or two.

My first cider was 6 gallons of fresh apple juice and champagne yeast. I loved it, but most people thought it was way too dry. Anyway, more for me!

I tried to make the second batch sweeter, so my wife could enjoy it too. So after the primary seemed over, I added some sugars. Which of course kickstarted fermentation again, so it just got stronger, and stayed dry. I tried again. Still stronger, still dry. Then I realized I was being an idiot. I threw it in a keg, chilled it way down to make the yeast as dormant as possible, THEN added some sugar, and tapped it. That stuff tasted really good, but was also well over 10% alcohol. Fine with me, but limited my wife to 1 or two glasses max, which kind of kills the point on a hot summer day.